Positional judgement | Game examples

The more I try to understand hex, the more I have the impression, that playing good game consists of 3 elements:

1) Calculating variants / brute force

2) Strong local play based on efficient shapes etc.

3) Positional judgement / strategic thinking

I would like to encourage some discussion regarding 3rd point. I don't want to go into endless details of different variants, but try to understand the direction of play, the way of thinking about hex especially after the fuseki / in the early chuban.

Game #1

What elements of the position do you consider crucial in planning the next move? What would be your way of thinking?

Link to the game: http://www.trmph.com/hex/game/lg-2000947

Force, in reality (2) and (3) are the same at different scales. An hex game is basically a giant local battle.

Regarding how to think about position, you can start to try to prove one player is winning. For example, pick a reasonable white choice and try to prove it's winning. You'll see that the proof is elusive, and you'll then try to amend your choice as white to look for another proof. And so on and so on. My first choice there is 12 F7, but it's just a starting point for thinking.

Basically is brute force plus nice short-cuts because all variations are almost identical to each other.

Lazy, if proving that one player wins would be so easy...I can rephrase my question and ask "how would you start proving, that one's winning a game".

It's kind of statistica, when you've lot of reasonable choices for each reasonable choice by opponent.

Ok, you can think about it like, simulations. You play a few simulated games and see winning rate.

Huh, what you just described is almost Monte Carlo tree search. Which I think is how leela works.

blikdak, or maybe i've described a "tree pruning" algorithm? in the end, all algorithms are quite the same.

Force, I will write down my thought process after seeing the pasted above position:

1) (5 seconds) top-left seems threatened: option = 12.d4

2) (1 minute) is it worth it or should be sacrificed? seems threatening because it possibly cannot be surrounded by black and maybe it revives j2

3) ok, well, for safety let's look at other options for another minute...

4) (1 minute) k3 and f7 are bridges and bridges are always good... but I don't see a point of any of those moves, I mean, no immediate threat.

5) (1 minute) e10 has merit, but how does it connect to left? let's run a quick simulation: http://www.trmph.com/hex/board#13,a8d3i5i10e9j2e3d10k4h6b6e10b11b7c9b10c10e5

6) not bad, let's run a simulation for previously picked 12.d4

7) (1 minute) http://www.trmph.com/hex/board#13,a8d3i5i10e9j2e3d10k4h6b6d4b3b4e5f7

8) desicion: either run those simulation further or just choose one. My decision is the more interesting one: 12.e10

I see I repeated lazyplayer's f7 without reading before. I discarded it without any analysis, only because it doesn't seem an immediate threat to me.

If I were to use more time I would run simulations on f7 too, but this one seems to need like 15 minutes of analysis, I cannot focus for that long :D

But what you are talking about, lazyplayer, is rather counting variants and simulations (whether with "prunning" or not). Whereas Force asked for tips and ideas on positional judgement / strategic thinking. So for me it would be an answer to the questions like "what does it mean to have a better position", "how do you evaluate positions" (but not in terms of counting all variations till the end of game and seeing who wins).

All in all, for other games like chess or go, there are plenty of books about every aspect of the game, positional judgement including. And in hex all we have is a few rules of thumb like "take corners", "make multi-purpose moves" etc. Is it the characteristic of this game that it is impossible to define some general rules or just we as players are too weak to spot and describe them?

struggler, players have ideas for rules, but their ideas differ. Nobody here is arrogant enough to write down the ideas which contradict other players ;)

I have noticed it ;) and I like it, of course. However, I would greatly appreciate it if there was any source of knowledge (which would be not an opinion of a particular player but rather a fact), something like a theory about this game. And I wonder why it has not appeared yet.

Because a fact would be something that can be proven. In hex the only proof is a brute force solution. We need opinions until some day we all just trust that leela bot is correct.

Well, one could say that it applies to all strategy games. Nevertheless, for chess or go which I mentioned earlier, there were whole books on that topic way before computers (and real brute force approaches) were in use.

> Is it the characteristic of this game that it is impossible to define some general rules or just we as players are too weak to spot and describe them?

We can spot them but there is no language to describe them. In chess and go they've invented a language to describe the most typical patterns. But there are millions more patterns that are known to strong players and have no name and no description. Most descriptions anyway are informal and they can't be codified into precise math language.

> I have noticed it ;) and I like it, of course. However, I would greatly appreciate it if there was any source of knowledge (which would be not an opinion of a particular player but rather a fact), something like a theory about this game. And I wonder why it has not appeared yet.

Because (almost) nobody has written books on hex. There is one book, which used some terminology like "ladders" and "templates", and these have come into common use. But I doubt use these concepts in my own play and I can't recommend them. Therefore, there is nothing that I can recommend really except copying our games and running simulations and trying to understand what's going on.

*But i don't use these concepts

I've to say, I learned hex by copying Maciej. Later I've also copied Arek in some aspects. Arek also copied from me and Maciej. The way to mastery goes through humble copying.

After you're experienced with all the typical plays that have already been invented, that is, once you've copied them in your games, you should start to look for variants and/or continuations. This is the only way to harass our 20 years of practical hex experience. If I win a few more games with leela (i doubt but I'll try) then maybe i'll write a book and you can pay me for that. :)

Another practical advantage of copying our initial stones is that you'll then have to focus on the endings, and the endings are much easier to analyze. You can see what's objectively right or wrong when the game is about to end. So not only you play better games, but you also learn more, because you stay focused on what can be learned (the ending). The beginning stones are really hard and I would say you should copy as much as possible until you're at our level.

I actually have written a "book" on hex that is currently in the editing phase, and I plan to put online soon (next few weeks). Of course there won't be anything of interest to the top level players, but I think (hope) it will be of use to anyone up to around the 2050 level. I think there's a fair amount of hex "knowledge" that fairly well known but simply hasn't been written down anywhere and I wanted to fix that :)

And as a bonus I'll probably learn a thing or two when Arek et al point out all the errors ;)

Happy, you can share the typography you've used. What tools you've used? :)

Wow, Hippo, that's great, can't wait to take a look!

Lazy: my first attempt was at using LaTeX, I even came up with a whole "package" for typesetting diagrams, however it was extremely slow, and this became tiresome as the book got longer. Instead I ended up making the "book" a website. I have a python script I wrote which takes a marked up html file and generates diagrams as svg images. All the diagrams in the book are fully interactive so the reader can step through the sequences or try alternate variations.

How long will be the boom HappyHippo?

Wow, HappyHippo, that's great :) can't wait to see it published! Will it be distributed free of charge?

And @lazyplayer - thanks for your hints, I'll give it a try ;)

It will be free

Great, thank you HappyHippo!

Arek, thank you very much for your insight, that is exactly what I was looking for! To be honest, I have also considered d4 and e10, however obvious f7 was my blind spot. Finally I have chosen e11 - why would you choose e10 instead of e11?

Force, I have no proof, but as a rule of thumb with ladders I don't "step down".

Talking facts, I would probably worry about this http://www.trmph.com/hex/board#13,a8d3i5i10e9j2e3d10k4h6b6e11g10

Game #2

What do you think should be white's plan? Which element of the position do you think are most important? How to utilize f1 stone?

Link to the game: http://www.trmph.com/hex/game/lg-2000926

At first sight I would think that you played the correct plan at that point, but i9 is probably incorrect.

The most important to me seems white h5 vs black i4, who plays first.

Utilizing f1 is through c3, not g2

Black looks overconnected to the bottom. There's probably not much to be gained from battling black on the bottom (below the g9 stone), though you may scrape a bit of influence. This means white's plan is what you did in the game: connect above the g9 stone, either between the h6 and g9 stones or else around the h6 stone. You don't want to commit to either of these, but rather, you want to strengthen both at once.

The top left corner is shouting out for a joseki. You played g2, which is decent, but I like c3 a bit better.

Lazyplayer: why is that?

Arek: When I see your comments they seem so obvious, however I couldn't see that in the game.

Force maybe it's by experience. I see this sequence in an instant http://www.trmph.com/hex/board#13,f1f1j9j4c4e9h6i9g9h5g6c3

I wouldn't even spend more than few moments on this, seems so forced/forcing (both)

Arek: probably that is the reason why there is such a gap between our ratings :P Anyway, thanks for your insights, as always very helpful :)

Force, good news is that those patterns literally repeat all the time so you will easily remember ;)

To disagree a little bit, I'm not a huge fan of 10.h5, or at least, it's not obviously the correct move. It creates a weakness on i5 which black might be able to exploit. I'd be looking at other options to see if any of them are better (maybe i3?)

Shalev, doesn't i3 has exactly the same weakness?

Why nobody likes 10 g2? Everyone ignores it? What's problem with that? :)

Force, i9 usually loses to this: http://www.trmph.com/hex/board#13,f1f1j9j4c4e9h6i9j8

it's possible that by playing g9, probably made another error and returned the favor so to speak.

laz, this family of things http://www.trmph.com/hex/board#13,f1f1j9j4c4e9h6i9g9g2i4j2l2k3i2i3g4h3g3h2d2

Maybe creator of leela could arrange such position and have a deciding vote :D

Arek, http://www.trmph.com/hex/board#13,f1f1j9j4c4e9h6i9g9g2i4j2l2k3i2i3g4h3g3h2d2d3c3d4c5h5f6e8

Lazy, this is very similar to options that I've analyzed during the game.

d2 is wrong, you need b3

Also the move order is all wrong, you should play like this, at least intuitively (I didn't check in detail)

@shalev, I think as white I'm delighted about black f2... I didn't run any analysis on the h5 response, but the point is to just tenuki and live better life than 1 move before. At least in my eyes the tradeoff of g2/f2 is favourable for white.

b3 instead of d2 is true, again, I didn't run any analysis. Just thinking g2 in general is terrible vs a black top-left move